How to do System dynamics simulations / diagrams in Mathematica?

Question

System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system. What makes using system dynamics different from other approaches to studying complex systems is the use of feedback loops and stocks and flows. These elements help describe how even seemingly simple systems display baffling nonlinearity

Here is how a system diagram looks like:

Apperently I should be able to this with System Modeler by loading this modelica library but I am also told here that:

The downside, as I understand it, is that each different use of a System Dynamics symbol requires its own entry in the library. For example, a stock with one inflow and one outflow requires a different Modelica symbol from one with one inflow and 2 outflows. Also (again, as I understand it), every separate equation requires its own symbol to be defined and added to the library before it can be used.

¿Anyone here can confirm or deny this? ¿Is this a limitation inherent in all Modelica enviroments? ¿or it is an implementation limitation on this particular library?

and, going back to the original aim of this question: Is there a less expensive way (than System Modeler) to do this in Mathematica, without System Modeler?

Answer 1

The limitation you quote is not a general limitation of Modelica. It is possible to define a Modelica component that has a variable number of inputs/outputs. Typically the number of inputs/outputs is then given by a parameter to that component.

For example, the following component has one input but 2 outputs, varied with the parameter nout:

model SIMO "Single input, multiple output"
  parameter Integer nout=2 "Number of outputs";
  RealInput u "Connector of Real input signal";
  RealOutput y[nout] "Connector of Real output signals";
equation
  {{{your equations}}}
end SIMO;

I have not used the System Dynamics modelica library, so cannot speak to how they have chosen to implement their interfaces.

It would be fully possible to create your custom models in Mathematica by defining equations from the ground up, and then simulating them using for example NDSolve. This would however require a significant amount of manual labor.

If you want to stay in the Wolfram product universe, SystemModeler would be the way to go. It allows you to simulate and interact with models from Mathematica, using a Mathematica package bundled with the product.

An overview of features of the Mathematica package, called WSMLink, can be found at http://wolfram.com/system-modeler/features/analysis-mathematica.html.

Documentation to see how the package actually is used is found at http://reference.wolfram.com/system-modeler/WSMLink/guide/WSMLink.html.